Linearity and efficiency are competing design factors in modern radio frequency (RF) power amplifiers; linearity is required to prevent symbol, constellation and/or frequency spectrum corruption and efficiency results in less power consumption, which is particularly significant in battery operated devices. Unfortunately, linearity and efficiency are mutually exclusive in RF power amplifiers, i.e., efficiency is greatest at operating points of the power amplifier where the amplifier input/output relationship is the least linear. Predistortion is one of several techniques by which a balance is struck between linearity and efficiency.
The complex gain GD of a power amplifier may be quantified by the ratio of the output signal of the power amplifier Y by the input signal X provided to the power amplifier, e.g.,
                                          G            D                    =                                    Y              X                        =                                                                                Y                    Re                                    +                                      j                    ⁢                                                                                  ⁢                                          Y                      Im                                                                                                            X                    Re                                    +                                      j                    ⁢                                                                                  ⁢                                          X                      Im                                                                                  =                                                                    A                    D                                    ⁢                                      ⅇ                                          j                      ⁢                                                                                          ⁢                                              θ                        D                                                                                            =                                                      G                    Re                                    +                                      j                    ⁢                                                                                  ⁢                                          G                      Im                                                                                                          ,                            (        1        )            where AD is amplitude distortion and θD is phase distortion. Computing this ratio is required repeatedly in predistortion calibration in that AD and θD are data dependent (or, more aptly, output power dependent, but output power is a typically a function of the input data). With advances in technology toward more robust calibration solutions, circuitry that implements a complex divider that computes the ratio in Eq. (1) is incorporated on devices in which the power amplifier is installed. Accordingly, ongoing research and development efforts seek ever greater reductions in resource consumption for such complex division.
One conventional complex division technique implements a change of coordinate system from Cartesian to polar, followed by division and subtraction operations, followed by a return to Cartesian coordinates, (since a vast majority of radio circuits process data in separate in-phase (I) and quadrature (Q) channels for real and imaginary parts, respectively, of the complex signal). Mathematically, such division proceeds as follows:
                              G          D                =                                                            Y                Re                            +                              j                ⁢                                                                  ⁢                                  Y                  Im                                                                                    X                Re                            +                              j                ⁢                                                                  ⁢                                  X                  Im                                                              =                                                                                        Y                                                  ⁢                                  ⅇ                                      j                    ⁢                                                                                  ⁢                    θ                                                  ⁢                Y                                                                                X                                                  ⁢                                  ⅇ                                      j                    ⁢                                                                                  ⁢                    θ                                                  ⁢                X                                      =                                                                                                    Y                                                                                                X                                                                      ⁢                                  ⅇ                                      j                    ⁡                                          (                                                                        θ                          Y                                                -                                                  θ                          X                                                                    )                                                                                  =                                                G                  Re                                +                                  j                  ⁢                                                                          ⁢                                                            G                      Im                                        .                                                                                                          (        2        )            The most apparent disadvantage of this approach is the requirement of the change in coordinates, which is typically carried out by a coordinate rotation digital computer (CORDIC) or similar technique.
Another conventional complex division technique multiplies the numerator and denominator of the ratio by the complex conjugate of the denominator followed by a complex multiplication operation and a real division operation, e.g.,
                              G          D                =                                                                              Y                  Re                                +                                  j                  ⁢                                                                          ⁢                                      Y                    Im                                                                                                X                  Re                                +                                  j                  ⁢                                                                          ⁢                                      X                    Im                                                                        ⁢                                                            X                  Re                                +                                  j                  ⁢                                                                          ⁢                                      X                    Im                                                                                                X                  Re                                +                                  j                  ⁢                                                                          ⁢                                      X                    Im                                                                                =                                                                      (                                                            Y                      Re                                        +                                          j                      ⁢                                                                                          ⁢                                              Y                        Im                                                                              )                                ⁢                                  (                                                            X                      Re                                        -                                          j                      ⁢                                                                                          ⁢                                              X                        Im                                                                              )                                                                              X                  Re                  2                                +                                  X                  Im                  2                                                      =                                          G                Re                            +                              j                ⁢                                                                  ⁢                                                      G                    Im                                    .                                                                                        (        3        )            
This technique also requires a data conversion, i.e., conversion of the denominator from a complex value to a real value, in order to obtain the solution. Thus, both of these techniques require resources for data conversion in the computation, as well as a division operation, which is among the most resource intensive mathematical operations performed by a machine.
Given the state of the current art, the need is apparent for computing complex division for complex gain calculation that avoids preliminary or preparatory data conversion operations as well as the division operation itself.